Geometrical and topological data representing three-dimensional components are used in CAD for obtaining mechanical layouts, examining mechanical interferences, etc. primarily in the automotive and aerospace industries. The amount of CAD data generally increases as the degree of details increases, sometimes surpassing the hardware capacity. A PC with Microsoft Windows™ normally has a limited capacity of 2 GB, unable to read in a massive amount of CAD data.
A method for handling such a massive amount of data includes, for example, conversion of a three-dimensional shape to triangles. This type of method approximates a three-dimensional shape with triangles within a specified tolerance with respect to the CAD data precisely representing the three-dimensional shape in terms of geometry and topology. Such a task of generating polygons is generally done by dividing a region into polygonal sections. In this case, however, the data get duplicated because both the CAD data and the polygons data need to be held in the memory. In addition, dividing a region into polygonal sections requires a significant amount of processing load; thus, it takes a longer real time.
In order to circumvent the disadvantages as above, numerous methods have been proposed. In one method, for example, once-obtained polygons data are stored in the memory and called when a real time display of the geometrical shape is needed, thereby eliminating recalculation. However, when high accuracy is required, that is, when the errors of the polygons data with respect to the original CAD data are required to be small, the amount of the polygons data increases tremendously, slowing down the display processing each time a viewing direction is changed. The amount of data increases exponentially with the inverse of the required tolerance value, that is, the smaller the required tolerance is, the more drastically the amount of data increases.
Therefore, a method for displaying a three-dimensional object represented by CAD data, wherein the memory size is small, accuracy is satisfactory, and the data can be read in fast, is desired.